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We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…
In the work two ways of evolutionary interpretation of entropy model for correspondence matrix calculation are proposed. Both approaches based on the stochastic chemical kinetic evolution under the detailed balance condition. The first…
We carry out the dynamical system analysis of interacting dark energy-matter scenarios by examining the critical points and stability for not just the background level cosmological evolution, but at the level of the linear density…
The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…
Non-equilibrium real-space condensation is a phenomenon in which a finite fraction of some conserved quantity (mass, particles, etc.) becomes spatially localised. We review two popular stochastic models of hopping particles that lead to…
We describe a systematic approach to construct coarse-grained Markov state models from molecular dynamics data of systems driven into a non-equilibrium steady state. We apply this method to study the globule-stretch transition of a single…
We introduce a simple model of a growing system with $m$ competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical…
In this work, we study the pattern solutions of doubly nonlocal logistic map that include spatial kernels in both growth and competition terms. We show that this map includes as a particular case the nonlocal Fisher-Kolmogorov equation, and…
Exchange-driven growth is a process in which pairs of clusters interact and exchange a single unit of mass. The rate of exchange is given by an interaction kernel $K(j,k)$ which depends on the masses of the two interacting clusters. In this…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
We study the evolution under their self-gravity of infinite ``shuffled lattice'' particle distributions, focussing specifically on the comparison of this evolution with that of ``daughter'' particle distributions, defined by a simple…
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing…
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…
We consider a parametric nonlinear nonhomogeneous elliptic equation, driven by the sum of two differential operators having different structure. The associated energy functional has unbalanced growth and we do not impose any global growth…
Exchange-driven growth (EDG) is a process in which pairs of clusters interact by exchanging single unit with a rate given by a kernel $K(j,k)$. Despite EDG model's common use in the applied sciences, its rigorous mathematical treatment is…
The Vlasov equation is analyzed for coarse grained distributions resembling a finite width of test-particles as used in numerical implementations. It is shown that this coarse grained distribution obeys a kinetic equation similar to the…
A dynamical version of the Widom-Rowlinsom model in the continuum is considered. The dynamics is modelled by a spatial two-component birth-and-death Glauber process where particles, in addition, are allowed to change their type with density…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…